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Some New Difference Inequalities and an Application to Discrete‐Time Control Systems

Author

Listed:
  • Hong Zhou
  • Deqing Huang
  • Wu-Sheng Wang
  • Jian-Xin Xu

Abstract

Two new nonlinear difference inequalities are considered, where the inequalities consist of multiple iterated sums, and composite function of nonlinear function and unknown function may be involved in each layer. Under several practical assumptions, the inequalities are solved through rigorous analysis, and explicit bounds for the unknown functions are given clearly. Further, the derived results are applied to the stability problem of a class of linear control systems with nonlinear perturbations.

Suggested Citation

  • Hong Zhou & Deqing Huang & Wu-Sheng Wang & Jian-Xin Xu, 2012. "Some New Difference Inequalities and an Application to Discrete‐Time Control Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:214609
    DOI: 10.1155/2012/214609
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    Cited by:

    1. Qinglong Wang & Zhijun Liu, 2013. "Uniformly Asymptotic Stability of Positive Almost Periodic Solutions for a Discrete Competitive System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. Limian Zhao & Shanhe Wu & Wu-Sheng Wang, 2014. "A Generalized Nonlinear Volterra‐Fredholm Type Integral Inequality and Its Application," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Wu-Sheng Wang & Shanhe Wu, 2013. "Some Difference Inequalities for Iterated Sums with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Yange Huang & Wu-Sheng Wang & Yong Huang, 2014. "A Class of Volterra‐Fredholm Type Weakly Singular Difference Inequalities with Power Functions and Their Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    5. Ricai Luo & Wu-Sheng Wang & Honglei Xu, 2014. "Estimation of Unknown Functions of Iterative Difference Inequalities and Their Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    6. YongZhou Qin & Wu-Sheng Wang, 2013. "A Generalized Nonlinear Sum‐Difference Inequality of Product Form," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    7. Yusong Lu & Wu-Sheng Wang & Xiaoliang Zhou & Yong Huang, 2014. "Generalized Nonlinear Volterra‐Fredholm Type Integral Inequality with Two Variables," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    8. Zongyi Hou & Shanhe Wu & Wu-Sheng Wang, 2014. "Some Retarded Difference Inequalities of Product Form and Their Application," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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